On a general system-partitioning in the many-electron correlation problem

General system partitioning in the many-electron correlation problem for atomic and molecular systems is addressed within the spinshift formalism. The conventional method of the unitary group subduction coefficient expansion is reconsidered in the latter framework and an orbital-level factorization of the coefficients is obtained. “Group-spinshifts” are introduced and exploited to propose an alternative method of generating states adapted to arbitrary subduction chains. © 1996 John Wiley & Sons, Inc.     

Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17x10(9) determinants in the active space, could not be performed.     

Electronic wave function of methane C---H bond orbital

Using the delocalized bond orbital method, obtained as a linear combination of the sp³ hybrid orbitals on the carbon and 1s orbitals on the hydrogens, we have calculated the energy of methane at the distances 0·9, 1·1 and 1·3 Å as a function of the orbital exponents. A discussion is given of the results in relation to the method of using a monocentric wave function on the carbon.

The energy at 1·1 Å is −40·122 a.u. and is in a rather good agreement with the results obtained by Mills and recently by Saturno and Parr.

The error with respect to the experimental value (0·4 a.u.) is of the order of the correlation energy.     

New bosonic excitation operators in many-electron wave functions

New excitation operators which have perfect bosonic symmetry are constructed for many-electron wave functions by regarding the system of many electrons as that of many species of bosons. Any electronic configurations can be generated by the new bosonic “void” operators. A coherent state is constructed with the bosonic operators and is adopted as a trial function for the time-dependent variational principle. The equation of motion which has exactly the same form as Hamilton's equation in classical mechanics is obtained with the complex variational parameters, the number of which is equal to the number of electrons. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 71–75, 1998     

One-particle correlation function in evanescent wave dynamic light scattering

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.     

Synthesis,molecular structures and PMR spectra of heteronuclear niobocene derivatives containing a niobium-tin bond

Treatment of niobocene carbonylhydride, Cp₂Nb(CO)H (I), with Ph_nSnCl_4?n and Et₂SnCl₂ in THF in the presence of Et₃N leads to the respective heteronuclear complexes Cp₂Nb(CO)SnR_nCl_3?n (R = Ph, n = 3 ÷ 1 (II–IV), R = Et, n = 2 (V)). Treatment of II with HCl in ether gives Cp₂Nb(CO)SnCl₃ (VI). Complex VI and its analog (MeC₅H₄)₂Nb(CO)SnCl₃ (VIII) were prepared by an alternative synthesis using direct reaction of I or (MeC₅H₄)₂Nb(CO)H with an equimolar quantity of SnCl₄ in THF in the presence of Et₃N. Complex VI is also generated by insertion of SnCl₂ into the NbCl bond in Cp₂Nb(CO)Cl (VII). X-Ray analysis of complexes II and VIII was performed: for II, space group P2₁/n, a = 10.1021(21), b = 17.4633(32), c= 14.2473(29) Å, β = 95.578(16)°, Z = 4; for VIII, space group. P2₁/n, a= 8.9369(15), b = 13.3589(12), c = 13.9292(20) Å, β = 99.490(14)°, Z = 4. The NbSn bond in VIII (2.764(9) Å) is shorter than that in II (2.825(2) Å). In both cases the NbSn bond is significantly shorter than the sum of Nb and Sn covalent radii (1.66 + 1.40 = 3.06 Å). It is probably partly multiple in character owing to an additional interaction of the lone electron pair of the Nb^III ion (d² configuration) with the antibonding Sn orbitals. The PMR spectra of II–VI exhibit two satellites of the singlet of C₅H₅ protons because of HSn¹¹⁷ and HSn¹¹⁹ spin-spin coupling (SSC). The SSC constant correlates with the number of electronegative chlorine atoms on the Sn atom.     

Hybridization and correlation in a model calculation of a two-electron bond

The paper presents a quantitative examination of some aspects of the molecular two-electron problem, using a calculation for a two-electron homonuclear bond based on a restricted set of one 2s and one 2p orbital per nucleus. The single-determinant approximations with pure 2s STO's and with hybrid AO's are considered, as well as “partial” configuration mixing (CI) over MO's involving one hybrid per atom and “complete” CI over the whole four-orbital basis. The calculations simulate an exact calculation as regards hybridization and (left-right) correlation effects. These are studied, for the lowest state, at various distances, introducing the axial electron density as a means for interpreting quantitatively the various effects. The importance of orthogonalizing the 2s AO's to the corresponding 1s AO's and the MO's used to the MO formed by 1s AO's is reviewed, pending further numerical analysis.     

The nature of electron correlation in a dissociating bond

We have constructed the unrestricted Hartree-Fock (UHF), restricted Hartree-Fock (RHF), and full configuration interaction (FCI) position and momentum intracules and holes for H···H at bond lengths R from 1 to 10 bohrs. We trace the recently discovered inversion of the UHF position hole at intermediate R to over-localization of the spin-orbitals, and support this by a correlation energy component analysis. The RHF and UHF momentum holes are found to be more complicated; however their features are explained through decomposition of electron correlation effects. The UHF momentum hole is also found to invert and exhibits interesting behavior at large R. The RHF (but not UHF) and FCI momentum intracules exhibit Young-type interference patterns related to recent double photoionization experiments. Our analyses yield the most comprehensive picture to date of the behavior of the electrons during homolytic bond fission.     

Lagrangian many-electron molecular dynamics—A modern tool for attacking the chemical bond: The physics behind the equations

The bona fide method of classical dynamics on a manifold of quantum chemical variational parameters such as, for instance, linear combination of atomic orbital (LCAO) and configuration interaction (CI) coefficients, exponents, and centers of the basis-set atomic orbitals (AO) that mimics quantum propagation of a state vector is elaborated toward understanding the physics which underlies this dynamics. © 1996 John Wiley & Sons, Inc.     

Analysis of molecular orbital wave functions in terms of valence bond functions for molecular fragments. I. Theory

A method of expansion of molecular orbital wave functions into valence bond (VB ) functions is extended to molecular fragments. The wave function is projected onto a basis of mixed determinants, involving molecular orbitals as well as fragment atomic orbitals, and is further expressed as a linear combination of VB functions, characteristic of structural formulas of the fragment but whose remaining bonds are frozen. Structural weights for the fragment are deduced from this expression. Delocalized molecular orbitals are used as a startpoint, as they are after an ordinary SCF calculation. Wave functions of medium-sized molecules may be analyzed with reasonable storage requirements in a computer.     

Effects of wave function modifications on calculated carbon–hydrogen bond lengths

The two-level factorial design (FD) and principal component analysis (PCA) chemometric techniques were used to investigate the carbon–hydrogen bond lengths dependence on the basis set size and quantum chemistry method, for H–C≡CH, H–C≡CF, H–C≡CCH₃, H–C≡CCN, H–C≡CCl and H–C≡CCCH molecular systems. The calculations were performed by using Hartree-Fock (HF), Møller-Plesset 2 (MP2) and Density Functional Theory (DFT) with B3LYP exchange-correlation functional methods. The effects concerning basis set size include the number of valence and polarization functions as well as the cooperative effect between them, at all computational levels. The increase in the number of valence functions decreases the calculated C–H bond lengths by approximately 0.0022 Å, while the inclusion of polarization functions at HF and B3LYP levels increases the C–H bond length, in contrast to the behavior obtained at MP2 level. The effect of the inclusion of diffuse functions is non-significant, at all three computational levels. Moreover, the valence–polarization interaction effects are not significant, except at the MP2 calculational level, in which such effects lead to an increase in the calculated C–H bond lengths. When the computational level changes from HF→B3LYP and B3LYP→MP2 the calculated C–H bond length values increase (on average) by +0.0100 and +0.0027 Å, respectively. Algebraic models (one for each level of calculation) successfully employed to reproduce the calculated values for H–C≡N bond length, a system not included in the training set. The HF/6-31G(d,p) and HF/6-31++G(d,p) results yield the lowest standard errors (0.0015 and 0.0014 Å, respectively) and correspond to the calculated points in closest proximity to the experimental one.     

Extracting elements of molecular structure from the all-particle wave function

Structural information is extracted from the all-particle (non-Born-Oppenheimer) wave function by calculating radial and angular densities derived from n-particle densities. As a result, one- and two-dimensional motifs of classical molecular structure can be recognized in quantum mechanics. Numerical examples are presented for three- (H(-), Ps(-), H(2)(+)), four- (Ps(2), H(2)), and five-particle (H(2)D(+)) systems.     

Preparation and molecular structures of 9,10-dihydrophenanthrenes: substituent effects on the long bond length

9,10-Dihydrophenanthrene derivatives 1-3 with electron-donating and/or -accepting groups at their 9,10-positions were prepared, and their precise molecular structures were determined by X-ray analyses at 203 K. The long C(9)-C(10) bond [1.646(4) A] in the hexaarylethane-type compound 1 with four electron-donating groups is mainly caused by steric interaction. Push-pull type substitution does not induce the elongation of the central bond in the present system; the corresponding distance in 9, 9-bis(4-dimethylaminophenyl)-10,10-dicyano derivative 2 [1.599(4) A] is intermediate between those of 1 and the tetracyano compound 3 [1. 587(2) A].     

Note on the space part of anti-symmetric wave functions in the many-electron problem

It is pointed out that if a many-electron antisymmetric wave function is expanded as a sum of spin-product functions, each multiplied by a function of coordinates, the resulting functions of coordinates have many of the same useful features found with the symmetric and antisymmetric functions representing singlet and triplet states in a two-electron system. For finding the energy, or any function of coordinates only, in the approximation in which spin-orbit interaction is neglected, one such function of coordinates can be used, the spins being disregarded. Simple procedures allow one to find matrix components of such operators as S ² and L . S from the functions of coordinates. These procedures are much easier to visualize than the use of projection operators, the permutation group, or other methods in current use. The general procedures are illustrated by application to the three-electron problem of the lithium atom, as treated by Lunell, Kaldor, and Harris, and their application to the contact hyperfine structure is pointed out.     

Computation of correlation functions and wave function projections in the context of quantum trajectory dynamics

The de Broglie-Bohm formulation of the Schrodinger equation implies conservation of the wave function probability density associated with each quantum trajectory in closed systems. This conservation property greatly simplifies numerical implementations of the quantum trajectory dynamics and increases its accuracy. The reconstruction of a wave function, however, becomes expensive or inaccurate as it requires fitting or interpolation procedures. In this paper we present a method of computing wave packet correlation functions and wave function projections, which typically contain all the desired information about dynamics, without the full knowledge of the wave function by making quadratic expansions of the wave function phase and amplitude near each trajectory similar to expansions used in semiclassical methods. Computation of the quantities of interest in this procedure is linear with respect to the number of trajectories. The introduced approximations are consistent with approximate quantum potential dynamics method. The projection technique is applied to model chemical systems and to the H+H(2) exchange reaction in three dimensions.     

Synthesis by Si-H bond lithiation of novel half-pincer and pincer silyllithium compounds and their molecular structures

Structural Chemistry - The synthesis and the X-ray structural analysis of novel pincer and half-pincer silyllithiums: Ar2 (N)(tBu2MeSi)SiLi (Ar(N) = o-dimethylbenzylamine) (2a),...